Solar Surface Dynamics convection & waves Bob Stein - MSU Dali Georgobiani - MSU Dave Bercik - MSU Regner Trampedach - MSU Aake Nordlund - Copenhagen Mats Carlsson - Oslo Viggo Hansteen - Oslo Andrew McMurry - Oslo Tom Bogdan - HAOO

The solar atmosphere is dynamic, But we don’t apply that knowledge. Static models are overly simplistic & give an inaccurate picture.

Observed Dynamics: Granulation white light image

P-Mode Oscillations Doppler velocity image

Magnetic Coronal Loops Emission traces magnetic field lines

Waves: what is observable Tgas (dashed), Trad (solid) Horizontal lines are means, which preferentially sample high temperatures because source function is non-linear function of temperature.

Chromospheric Temperature: hot or cold Get enhanced emission without enhanced gas temperature, because source function preferentially samples high temperatures.

Proton density: Equilibrium (dashed), Non-equilibrium (solid)

Shocks: Ionization & Recombination

Mean Atmosphere Inhomogeneous T (see only cool gas), P turb Raises atmosphere 1 scale height

Never See Hot Gas

Simulations

Two Calculations 1. 3D, compressible, mhd 2. 1D, non-LTE radiation hydro-dynamics

Computation Solve –Conservation equations mass, momentum & internal energy –Induction equation –Radiative transfer equation 3D, Compressible EOS includes ionization Open boundaries –Fix entropy of inflowing plasma at bottom

Equations

Method Spatial derivatives - Finite difference –6 th order compact or 3 rd order spline Time advance - Explicit –3 rd order predictor-corrector or Runge-Kutta Diffusion

Boundary Conditions Periodic horizontally Top boundary: Transmitting –Large zone, adjust <   mass flux, ∂u/∂z=0, energy ≈ constant, drifts slowly with mean state Bottom boundary: Open, but No net mass flux –(Node for radial modes so no boundary work) –Specify entropy of incoming fluid at bottom –(fixes energy flux) Top boundary: B  potential field Bottom boundary: inflows advect 1G or 30G horizontal field, or B vertical

Wave Reflection Acoustic Wave Gravity wave

Radiation Transfer LTE Non-gray - multigroup Formal Solution Calculate J - B by integrating Feautrier equations along one vertical and 4 slanted rays through each grid point on the surface.

Simplifications Only 5 rays 4 Multi-group opacity bins Assume  L  C

Opacity is binned, according to its magnitude, into 4 bins.

Line opacities are assumed proportional to the continuum opacity Weight = number of wavelengths in bin

Wavelengths with same  (z) are grouped together, so integral over  and sum over commute Advantage integral over  and sum over commute

Advantage Wavelengths with same  (z) are grouped together, so integral over  and sum over commute

Initial Conditions Snapshot of granular convection (6x6x3 Mm) –Resolution: 25 km horizontally, km vertically 1G or 30G horizontal seed field, or 400 G vertical field, imposed

Solar Magneto-Convection

Energy Fluxes ionization energy 3X larger energy than thermal

Fluid Parcels reaching the surface Radiate away their Energy and Entropy Z S E  Q 

Entropy Green & blue are low entropy downflows, red is high entropy upflows Low entropy plasma rains down from the surface

Plasma cooled at surface is pulled down by gravity

A Granule is a fountain velocity arrows, temperature color

Stratified convective flow: diverging upflows, turbulent downflows Velocity arrows, temperature fluctuation image (red hot, blue cool)

Vorticity Downflows are turbulent, upflows are more laminar.

Velocity at Surface and Depth Horizontal scale of upflows increases with depth.

Stein & Nordlund, ApJL 1989

Upflows are slow and have nearly the same velocity.

Upflows diverge. Fluid reaching surface comes from small area below the surface

Downflows are fast. In 9 min some fluid reaches the bottom.

Downflows converge. Fluid from surface is compressed to small area below surface

Vorticity surface and depth.

Turbulent downdrafts

Velocity Spectrum

Velocity Distribution Up Down

Entropy Distribution

Vorticity Distribution Down Up

Magnetic Field Reorganization

Simulation Results: B Field lines

Field Distribution simulation observed Both simulated and observed distributions are stretched exponentials.

Exponential Distribution

Flux Emergence & Disappearance

Emerging Magnetic Flux Tube

Magnetic Field Lines, t=0.5 min

Magnetic Field Lines, t=1.0 min

Magnetic Field Lines, t=1.5 min

Magnetic Field Lines, t=2.0 min

Magnetic Field Lines, t=2.5 min

Magnetic Field Lines, t=3.0 min

Magnetic Field Lines, t=3.5 min

Magnetic Field Lines, t=4.0 min

Magnetic Field Lines, t=4.5 min

Magnetic Field Lines, t=5.0 min

Magnetic Field Lines, t=5.5 min

Magnetic Field Lines: t=6 min

Magnetic “Flux Tube” Fieldlines

“Flux Tube” Evacuation V xz + B

“Flux Tube” Evacuation field lines + density fluctuations

Micropores David Bercik - Thesis

Strong Field Simulation Initial Conditions –Snapshot of granular convection (6x6x3 Mm) –Impose 400G uniform vertical field Boundary Conditions –Top boundary: B -> potential field –Bottom boundary: B -> vertical Results –Micropores

Micropore Intensity image + B 0.5 kG intervals (black) + V z =0 contours (red).

“Flux Tube” Evacuation field + temperature contours

“Flux Tube” Evacuation field + density contours

Comparison with Observations

Observables

Solar velocity spectrum MDI doppler (Hathaway) TRACE correlation tracking (Shine) MDI correlation tracking (Shine) 3-D simulations (Stein & Nordlund) v ~ k v ~ k -1/3

Line Profiles Line profile without velocities. Line profile with velocities. simulation observed

Convection produces line shifts, changes in line widths. No microturbulence, macroturbulence. Average profile is combination of lines of different shifts & widths. average profile

Stokes Profiles of Flux Tube new SVST, perfect seeing

Stokes Profiles of Micropore intensity + slit

Granulation

Spectrum of granulation Simulated intensity spectrum and distribution agree with observations after smoothing with telescope+seeing point spread function.

Granule Statistics

Magnetic Field & Granules

Emergent Intensity, mu=0.5

Magnetic Field Strength

Emergent Intensiyt, mu=0.5

Emergent Intensity, mu=0.5

Stokes Image - Quiet Sun Synthetic Observation - La Palma Telescope MTF + Moderate Seeing Surface IntensityStokes V 6 Mm

Stokes Image - Quiet Sun Synthetic Observation - La Palma Telescope MTF + Excellent Seeing Surface IntensityStokes V 6 Mm

Stokes Image - Quiet Sun Synthetic Observation - Perfect Telescope & Seeing Surface IntensityStokes V 6 Mm

Atmospheric Dynamics

Dynamic Effects Non-linear effects –The mean of a dynamic atmosphere is not equal to a static atmosphere –e.g. Planck function is a non-linear function of temperature, (except in the infrared) – T rad > T gas Slow rates –Not enough time to reach equilibrium –e.g. Ionization and recombination slow compared to dynamic times in chromosphere electron density > than LTE

3D Effects Inhomogeneous T (see only cool gas), P turb Raises atmosphere 1 scale height

p-mode frequencies 1D Standard model 3D Convection model

P-Mode Excitation Modes are excited by PdV work of turbulent and non-adiabatic gas pressure fluctuations. Pressure fluctuation Mode compression Mode mass

P-Mode Excitation Triangles = simulation, Squares = observations (l=0-3) Excitation decreases both at low and high frequencies

Turbulent and Gas Pressure Most p-mode driving is primarily by turbulent pressure.

Excitation: Turbulence vs. Entropy

Excitation: Up vs. Down Flows

P-Mode Excitation

P-Mode excitation Decreases at low frequencies because of mode properties: –mode mass increases toward low frequencies –mode compression decreases toward low frequencies Decreases at high frequencies because of convection properties: –Turbulent and non-adiabatic gas pressure fluctuations produced by convection and convective motions are low frequency.

Impulsive Wave Generation Wave pulse Disappearing granule

Shocks Effect of radiation

Shocks: Effect of Radiation

Waves: observed & simulated

CaII H line: 1.39 Mm

CaII H line: 1.42 Mm

MHD Waves: reflection & mode coupling at beta=1 Incident acoustic fast modes. Transmitted magnetic fast modes + acoustic slow modes. Reflected acoustic fast modes

MHD Waves: Shocks+Radiation shocks & radiation decrease amplitude of reflected & transmitted waves interference pattern shows reflected waves

Fast & Slow MHD Waves, t=27.5 Fast magnetic wave Slow acoustic wave Waves generated by piston in low beta strong magnetic field.

Velocity || B, t=58.5 black lines=B, white lines = beta

Velocity B, t=58.5 s fast waves are refracting sideways & down

Fast & Slow MHD Waves - 2 Fast magnetic wave has passed through top of computational domain. It is being refracted to the side and back down. Slow acoustic wave propagates along B

Downward propagating fast waves couple to transmitted fast and slow waves at = 1 surface

Fast & Slow MHD Waves - 3 Slow acoustic wave shocks. Downward propagating fast magnetic wave couples to fast acoustic and slow magnetic waves at the beta=1 surface.

Next

New Code Conservation equations for Mass, momentum, internal energy, B Radiation Transfer - LTE H - opacity, few rays, fixed directions, no interpolation Equation of State Saha H ionization

Numerics 5 th order finite difference derivatives 3 rd order Runge-Kutta time advance –low memory Operates on planes –to fit in cache Parallelizes

The Future Supergranulation scale magneto-convection –What are supergranules? –Emergence of magnetic flux –Disappearance of magnetic flux –Maintenance of the magnetic network –Pores and sunspots

The End